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These notes were written for the old IB syllabus (2009). The new IB syllabus for first examinations 2016 can be accessed by clicking the link below.

### 15.2 - Born Haber cycles

15.2.1: Define and apply the terms lattice enthalpy and electron affinity

The enthalpy change when 1 mol of an ionic lattice is formed from its component ions at an infinite distance apart.

M+(g) + X-(g) -> MX(s)

The value of lattice enthalpy is understood to be negative for the formation of the lattice (an exothermic - bond forming process), and positive for the breaking up of the lattice (an endothermic - bond breaking process).

Hess' law can also be aplied to the formation of ionic lattices via a series of steps. In the case of ionic substances this is called a Born Haber cycle.

lattice enthalpy increases with higher ionic charge and with smaller ionic radius (due to increased force of attraction). The smaller the ion the greater its charge density and the force of electrostatic attraction that it can exert.

Lattice enthalpy may be seen defined in two different ways, depending on the reference literature. For the IB it is defined as the energy released when 1 mole of an ionic substance is formed from its constituent gaseous ions at infinite separation.

Na+(g) + Cl-(g) NaCl(s) ΔH = -ve

 Each ion exerts an electrostatic field that attracts the oppositely charged ions. The ions are all drawn together into a giant lattice in which every positive ion is surrounded by negative ions and vice-versa. The animation only shows the first few ions in the lattice, but the process continues until all of the ions formed in the reaction are arranged in rows and columns - a giant ionic lattice. The energy released on forming the lattice is more than enough to compensate for any energy needed to ionise the sodium (in this case).

15.2.2: Explain how the relative sizes and the charges of the ions on the lattice enthalpies affect the lattice enthalpies of different ionic compounds. The relative value of the theoretical lattice enthalpy increases with higher ionic charge and smaller ionic radius due to increased forces of attraction.

The bond between ions of opposite charge is strongest when the ions are small.

The lattice energies for the alkali metal halides is therefore largest for LiF and smallest for CsI, as shown in the table below.

Lattice Energies of Alkali Metals Halides (kJ/mol)

 F- Cl- Br- I- Li+ 1036 853 807 757 Na+ 923 787 747 704 K+ 821 715 682 649 Rb+ 785 689 660 630 Cs+ 740 659 631 604

The ionic bond should also become stronger as the charge on the ions becomes larger. The data in the table below show that the lattice energies for salts of the OH- and O2- ions increase rapidly as the charge on the ion becomes larger.

Lattice Energies of Salts of the OH- and O2- Ions (kJ/mol)

 OH- O2- Na+ 900 2481 Mg2+ 3006 3791 Al3+ 5627 15916

15.2.3: Construct a Born-Haber cycle for group 1 and 2 oxides and chlorides and use it to calculate an enthalpy change.

15.2.4: Discuss the difference between theoretical and experimental lattice enthalpy values of ionic compounds in terms of their covalent character. A significant difference between the two values indicates covalent character.

It is possible to measure lattice enthalpy using thermodynamic principles in the Born Haber cycle. However, it is also possible to calculate theoretical lattice enthalpy based on the electrostatic attractions between ions.

For the theoretical calculation some assumptions must be made:

1. The ions themselves are treated as point charges.

2. The structure is purely ionic

The overall lattice enthalpy is then a function of electrostatic attraction, the lattice structure, the magnitude of the charges on the ions. There are several approaches, the best known being the Madelung equation and the Kaperinsky equation:

Equations here

For highly electropositive metals the correlation between experimentally determined values and theoretically determined values is good. However, in some ionic compounds, such as silver chloride, there is a large difference. This suggests that such compounds are not purely ionic in their structure.

The classical comparison is between the halides of the group 1 metals and silver halides.

 compound theoretical lattice enthalpy/ kJ mol-1 experimental lattice enthalpy/ kJ mol-1 sodium chloride 766 771 silver chloride 770 905

The data shows that the assumptions made for the silver chloride lattice are probably not valid and that the structure has some contribution from covalent bonding. This appears to be bonding the stucture together more tightly, as in a giant covalent structure.

Curiously, the relative melting points indicate that the structure of silver chloride is actually weaker than that of sodium chloride. It seems as though the bonding changes its nature as the compound is heated and reverts back to a more ionic or simple covalent model.

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